- Contango is a price premium.
- Backwardation is a price lagging.
These concepts are applied only for the futures markets. In order to explain the idea, we will have to dig a bit into the theory and mathematical formulas.
The concept idea. Theory
Futures contracts were developed for hedging risks, connected with underlying assets. That is why, as a rule, the futures and spot prices are not equal but connected with each other by the following formula:
F = S * ert
- S – asset spot price,
- r – risk-free rate,
- t – time until the contract expiry,
- e – exponent.
In simple words it means that a trader should receive income for owning a futures. This income shouldn’t be lower than alternative risk-free variants – for example, deposits.
This formula doesn’t take into account expenditures on the commodity physical storage. However, if we consider commodity futures with a possibility of physical delivery (for example, on oil, metals, agricultural crops, etc.), then additional expenditures on physical storage should be taken into account. In such a case, the previous formula will change:
F = S * e(r + u) * t
where: U – annual storage cost
If the futures price coincides with the theoretical one (calculated by the formula), this market state is called ‘full carry’. In reality it means that the futures price takes into account all expenditures – the financial ones and those that are connected with storage.
However, in reality the futures price is often above or below the spot price. In such a case, the formula is supplemented with one more indicator – ‘convenience yield’ Y.
F = S * e(r + uy) * t
In fact, the ‘convenience yield’ is the benefit of physical ownership of a commodity in the spot market. This concept is applied only for commodity markets, because there could be a deficit or overabundance of physical commodities in them. Convenience yield couldn’t be applied to the financial markets because there cannot be a deficit of stock indices in them.
For example, it becomes very cold at the end of the winter, when fuel reserves are nearly exhausted. If it happens, the prices on the heating fuel or black oil fuel sharply grow. At such moments, it is more profitable to keep fuel in storages than to have futures on it.
Another example – if the summer is rainy and cold, some part of crops, for example, wheat, could be lost. If the physical amount of wheat decreases, there is a deficit of wheat and its price grows. In such a case it is also good to have wheat reserves in a storage.